The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 X+2 1 1 2 1 1 2 1 1 1 1 1 X 1 X X 1 1 1 2 1 1 1 0 1 2 1 0 1 1 1 1 0 2 1 X X X 1 1 1 1 1 1 0 1 X 1 1 1 1 0 2 1 1 1 1 1 1 1 1 X 1 0 X X+2 1 0 0 0 X+2 1 1 1 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 X+2 1 X+2 X+1 1 X+1 0 1 1 1 2 0 X+1 1 X+1 1 1 0 X+2 1 1 3 X X+3 1 3 1 1 1 2 X+1 X+3 X 1 1 X+2 1 1 1 X+1 0 X X+2 X+1 X+2 X 3 1 X 3 X+3 X+1 1 1 X+1 1 0 2 0 0 X+3 X 2 X+1 X 1 1 3 X 0 0 1 2 0 2 0 0 X 0 X+2 0 X+2 2 X X X 2 0 0 X+2 0 X X+2 2 2 X 2 X X X 0 0 X X+2 0 0 X+2 X 2 X X 0 2 X+2 X 2 X 2 2 X+2 X+2 0 0 X+2 0 X+2 0 0 2 2 X X+2 X+2 X 2 2 X X 0 0 X 0 2 0 X 0 X X+2 X+2 X X+2 X+2 X+2 X+2 X X+2 X X 2 X+2 2 X 0 0 0 2 0 0 0 2 2 0 2 2 2 0 0 2 2 0 0 0 2 0 2 2 2 0 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 2 0 0 0 2 2 0 2 0 2 0 2 0 2 2 0 0 0 0 0 0 2 2 0 2 0 2 2 2 0 2 0 0 0 2 0 0 2 2 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 2 0 2 2 2 0 0 2 2 2 2 2 0 2 0 0 2 2 2 0 2 0 0 2 0 0 2 0 0 0 0 0 2 2 2 2 0 2 0 0 2 2 0 0 0 2 0 0 0 2 2 2 2 0 2 0 0 2 2 2 0 2 2 2 0 2 0 2 0 0 0 0 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 2 2 0 2 2 0 2 0 0 0 0 2 2 2 0 0 2 2 2 2 0 0 0 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 0 2 0 2 2 2 0 0 2 2 2 2 0 0 2 0 2 0 0 0 2 0 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 0 2 2 2 2 0 2 0 0 2 2 0 2 2 2 0 0 2 0 2 2 0 0 0 2 2 0 0 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+76x^79+114x^80+260x^81+234x^82+410x^83+254x^84+432x^85+226x^86+368x^87+187x^88+356x^89+208x^90+304x^91+164x^92+188x^93+65x^94+100x^95+35x^96+28x^97+23x^98+14x^99+9x^100+12x^101+9x^102+8x^103+2x^104+4x^105+3x^106+1x^108+1x^112 The gray image is a code over GF(2) with n=348, k=12 and d=158. This code was found by Heurico 1.16 in 1.68 seconds.